The zip line park is about a 45 minute drive from Ajaccio and opens at 10:00. I know at least 3 drivers are sharing a cab to airport to pick up cars. I don't know if any will have space or not. Cars run around $120 so I would say $30plus gas money would be transpo cost. Park I think is 10 euros. Expect to stay 1.5 to 2.0 hours. Some drivers may come straight back to town and then drive along coastal road in afternoon. Others may stay near zip lines and go to the tortoise sanctuary.
As far as zip lining goes there are more things than zip lines. Think rope trails through the tree tops. Here is the website again with lots of great pictures.
http://www.revesdecimes.fr/ Maybe your cousin would like to come just to document your death defying feats for the family history books.